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Article(id=1245390262726406476, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0509, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1682265600000, receivedDateStr=2023-04-24, revisedDate=1686672000000, revisedDateStr=2023-06-14, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853776865, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853776865, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853776865, creator=13701087609, updateTime=1774853776865, updator=13701087609, issue=Issue{id=1245390255516397762, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='5', pageStart='1', pageEnd='231', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853775147, creator=13701087609, updateTime=1774854426342, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392986884911753, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392986889106058, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=93, endPage=107, ext={EN=ArticleExt(id=1245390262999036249, articleId=1245390262726406476, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Numerical analysis of influence factors on seismic performance of flexible connection AAC infilled wall steel frame, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to analyze the trend and significance of the influence of different factors on the seismic performance of flexible connection autoclaved areated concrete(AAC) masonry filled wall steel frame structures, the feasibility of the modeling method and parameters selection was verified based on the results of pseudo-static tests, nine orthogonal finite element models were established by ABAQUS, and variable parameter analysis was carried out on axial compression ratio, reserved seam width, spring stiffness and height span ratio of models. The results show that the effects of reserved joint width, stiffness of energy-consuming materials, height span ratio and axial compression ratio on seismic performance of the structure decrease successively. On the whole, it is beneficial to increase the reserved joint width, reduce the stiffness of energy-consuming materials, high span ratio and axial compression ratio to improve the seismic performance of the structure. In actual application, the recommended value for the joint width between flexible connection AAC wall and frames is around 40 mm, and the stiffness of the filler between reserved joints is between 100~500 N/mm.

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为分析不同因素变化对柔性连接蒸压加气混凝土（autoclaved areated concrete，AAC）砌体填充墙钢框架抗震性能影响的趋势和显著性，基于拟静力试验结果验证了建模方式及参数选取的可行性，采用ABAQUS建立9个有限元正交模型，对模型轴压比、预留缝宽、耗能材料刚度和高跨比进行变参分析。研究结果表明：预留缝宽、耗能材料刚度、高跨比和轴压比对结构抗震性能指标影响的显著性依次降低。整体上，增大预留缝宽，减小耗能材料刚度、高跨比以及轴压比对提高结构的抗震性能有利。实际应用中建议柔性连接AAC墙框间缝宽取值在40 mm左右，缝间填充材料的刚度宜在100~500 N/mm之间。

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王旭峰（1995—），男，助理工程师，硕士，主要从事结构抗震研究。E-mail：
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陈子夷（1997—），女，硕士研究生，主要从事结构加固研究。E-mail：

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陈子夷（1997—），女，硕士研究生，主要从事结构加固研究。E-mail：

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陈子夷（1997—），女，硕士研究生，主要从事结构加固研究。E-mail：

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(in Chinese), articleTitle=Study on Seismic behavior of autoclaved aerated concrete self insulation block walls, refAbstract=null), Reference(id=1245390280103407950, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, doi=null, pmid=null, pmcid=null, year=2011, volume=39, issue=7, pageStart=978, pageEnd=982, url=null, language=null, rfNumber=[27], rfOrder=44, authorNames=闫春岭, 唐益群, 刘莎, journalName=同济大学学报（自然科学版）, refType=null, unstructuredReference=闫春岭，唐益群，刘莎. 地铁荷载下饱和软黏土累积变形特性[J]. 同济大学学报（自然科学版），2011，39(7):978-982., articleTitle=地铁荷载下饱和软黏土累积变形特性, refAbstract=null), Reference(id=1245390280170516817, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, doi=null, pmid=null, pmcid=null, year=2011, volume=39, issue=7, pageStart=978, pageEnd=982, url=null, language=null, rfNumber=[27], rfOrder=45, authorNames=YAN Chunling, TANG Yiqun, LIU Sha, journalName=Journal of Tongji University (Natural Science), refType=null, unstructuredReference=YAN Chunling, TANG Yiqun, LIU Sha. Accumulative deformation characteristics of saturated soft clay under subway loading in Shanghai[J]. Journal of Tongji University (Natural Science), 2011, 39(7): 978-982. 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tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Fig. 16, caption=Relationship between four factors and various indicators, figureFileSmall=1CsoiW5si+yVNlOHdMBcTA==, figureFileBig=aFKs+FUln0VWISm+JcIa5g==, tableContent=null), ArticleFig(id=1245390273820340248, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=图16, caption=4个因素与各指标的关系, figureFileSmall=1CsoiW5si+yVNlOHdMBcTA==, figureFileBig=aFKs+FUln0VWISm+JcIa5g==, tableContent=null), ArticleFig(id=1245390273954557983, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Fig. 17, caption=Impact rate of assessment indicators by various factors, figureFileSmall=RgfR+jVQH8cjfLBsG74O/g==, figureFileBig=Jvy8adz8EtgR1ltC+sl9IA==, tableContent=null), ArticleFig(id=1245390274038444068, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=图17, caption=考核指标受各因素的影响率, figureFileSmall=RgfR+jVQH8cjfLBsG74O/g==, figureFileBig=Jvy8adz8EtgR1ltC+sl9IA==, tableContent=null), ArticleFig(id=1245390274147495979, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 1, caption=

Mechanical property of steels

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取样部位试件厚度（直径）/mm屈服强度/MPa抗拉强度/MPa强屈比伸长率/%
梁腹板64195441.3026.62
柱腹板84095391.3219.92
柱翼缘板103855281.3725.29
加劲肋144215451.2926.53
拉结钢筋65947631.2828.89
), ArticleFig(id=1245390274248159280, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表1, caption=

钢材力学性能

, figureFileSmall=null, figureFileBig=null, tableContent=
取样部位试件厚度（直径）/mm屈服强度/MPa抗拉强度/MPa强屈比伸长率/%
梁腹板64195441.3026.62
柱腹板84095391.3219.92
柱翼缘板103855281.3725.29
加劲肋144215451.2926.53
拉结钢筋65947631.2828.89
), ArticleFig(id=1245390274378182712, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 2, caption=

Masonry plastic parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
参数膨胀角/（°）偏心率双轴受压与单轴受压极限强度之比拉、压子午面上的第二应力不变量之比黏聚系数
取值300.11.160.6670.0005
), ArticleFig(id=1245390274487234622, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表2, caption=

砌体塑性参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数膨胀角/（°）偏心率双轴受压与单轴受压极限强度之比拉、压子午面上的第二应力不变量之比黏聚系数
取值300.11.160.6670.0005
), ArticleFig(id=1245390274613063748, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 3, caption=

Factors level

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水平影响因素
（因素A）轴压比（因素B）预留缝宽/mm（因素C）耗能材料刚度/（N/mm）（因素D）高跨比
10.13010001.17
20.2405000.90
30.3501000.81
), ArticleFig(id=1245390274696949833, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表3, caption=

因素水平表

, figureFileSmall=null, figureFileBig=null, tableContent=
水平影响因素
（因素A）轴压比（因素B）预留缝宽/mm（因素C）耗能材料刚度/（N/mm）（因素D）高跨比
10.13010001.17
20.2405000.90
30.3501000.81
), ArticleFig(id=1245390274806001743, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 4, caption=

Orthogonal table of model parameter schemes

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序号各影响因素的水平取值编号模型参数方案模型编号
因素A因素B因素C因素D
11111A1B1C1D1模型M1
21222A1B2C2D2模型M2
31333A1B3C3D3模型M3
42123A2B1C2D3模型M4
52231A2B2C3D1模型M5
62312A2B3C1D2模型M6
73132A3B1C3D2模型M7
83213A3B2C1D3模型M8
93321A3B3C2D1模型M9
), ArticleFig(id=1245390274881499218, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表4, caption=

模型参数方案正交表

, figureFileSmall=null, figureFileBig=null, tableContent=
序号各影响因素的水平取值编号模型参数方案模型编号
因素A因素B因素C因素D
11111A1B1C1D1模型M1
21222A1B2C2D2模型M2
31333A1B3C3D3模型M3
42123A2B1C2D3模型M4
52231A2B2C3D1模型M5
62312A2B3C1D2模型M6
73132A3B1C3D2模型M7
83213A3B2C1D3模型M8
93321A3B3C2D1模型M9
), ArticleFig(id=1245390274977968215, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 5, caption=

Calculation results of orthogonal model assessment indicators

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编号正交表考核指标
因素A因素B因素C因素DΔy/mmPmax/kNμK0/（kN/mm）Ee/（kN•m）Ep/（kN•m）
M111115.14360.7910.4927.811.06994.662
M212225.70378.5710.5124.781.06191.004
M313339.57362.996.8822.860.89787.238
M421236.09362.288.8728.861.33393.339
M522316.72344.148.9220.470.93487.967
M623126.92389.439.5424.200.89189.718
M731326.77308.447.8727.060.84569.948
M832135.93382.909.9826.251.07992.993
M933216.93370.189.4319.360.81188.029
), ArticleFig(id=1245390275095408733, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表5, caption=

正交模型考核指标计算结果

, figureFileSmall=null, figureFileBig=null, tableContent=
编号正交表考核指标
因素A因素B因素C因素DΔy/mmPmax/kNμK0/（kN/mm）Ee/（kN•m）Ep/（kN•m）
M111115.14360.7910.4927.811.06994.662
M212225.70378.5710.5124.781.06191.004
M313339.57362.996.8822.860.89787.238
M421236.09362.288.8728.861.33393.339
M522316.72344.148.9220.470.93487.967
M623126.92389.439.5424.200.89189.718
M731326.77308.447.8727.060.84569.948
M832135.93382.909.9826.251.07992.993
M933216.93370.189.4319.360.81188.029
), ArticleFig(id=1245390275191877729, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 6, caption=

Range analysis of orthogonal model assessment indicators

, figureFileSmall=null, figureFileBig=null, tableContent=
考核指标因素K1K2K3k1k2k3极差R
Δy/mm轴压比20.4119.7319.636.806.586.540.26
预留缝宽18.0018.3523.426.006.127.811.81
耗能材料刚度17.9918.7223.066.006.247.671.67
高跨比18.7919.3921.596.266.467.200.94
Pmax/kN轴压比1102.351095.851061.52367.45365.28353.8413.61
预留缝宽1031.511105.611122.60343.84368.54374.2030.36
耗能材料刚度1133.121111.031015.57377.71370.34338.5239.19
高跨比1075.111076.441108.17358.37358.81369.3911.02
μ轴压比27.8827.3327.289.299.119.090.20
预留缝宽27.2329.4125.859.089.808.621.18
耗能材料刚度30.0128.8123.6710.009.607.892.11
高跨比28.8427.9225.739.619.318.581.03
K0/（kN/mm）轴压比75.4573.5372.6725.1524.5124.220.93
预留缝宽83.7371.5066.4227.9123.8322.145.77
耗能材料刚度78.2673.0070.3926.0924.3323.462.63
高跨比67.6476.0477.9722.5525.3525.993.44
Ee/（kN•m）轴压比3.0273.1582.7351.0091.0530.9120.141
预留缝宽3.2473.0742.5991.0821.0250.8660.216
耗能材料刚度3.0393.2052.6761.0131.0680.8920.176
高跨比2.8142.7973.3090.9380.9321.1030.171
Ep/（kN•m）轴压比272.904271.024250.97090.96890.34183.6577.311
预留缝宽257.949271.964264.98585.98390.65588.3284.672
耗能材料刚度277.373272.372245.15392.45890.79181.71810.740
高跨比270.658250.670273.57090.21983.55791.1907.633
), ArticleFig(id=1245390275275763814, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表6, caption=

正交模型考核指标的极差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
考核指标因素K1K2K3k1k2k3极差R
Δy/mm轴压比20.4119.7319.636.806.586.540.26
预留缝宽18.0018.3523.426.006.127.811.81
耗能材料刚度17.9918.7223.066.006.247.671.67
高跨比18.7919.3921.596.266.467.200.94
Pmax/kN轴压比1102.351095.851061.52367.45365.28353.8413.61
预留缝宽1031.511105.611122.60343.84368.54374.2030.36
耗能材料刚度1133.121111.031015.57377.71370.34338.5239.19
高跨比1075.111076.441108.17358.37358.81369.3911.02
μ轴压比27.8827.3327.289.299.119.090.20
预留缝宽27.2329.4125.859.089.808.621.18
耗能材料刚度30.0128.8123.6710.009.607.892.11
高跨比28.8427.9225.739.619.318.581.03
K0/（kN/mm）轴压比75.4573.5372.6725.1524.5124.220.93
预留缝宽83.7371.5066.4227.9123.8322.145.77
耗能材料刚度78.2673.0070.3926.0924.3323.462.63
高跨比67.6476.0477.9722.5525.3525.993.44
Ee/（kN•m）轴压比3.0273.1582.7351.0091.0530.9120.141
预留缝宽3.2473.0742.5991.0821.0250.8660.216
耗能材料刚度3.0393.2052.6761.0131.0680.8920.176
高跨比2.8142.7973.3090.9380.9321.1030.171
Ep/（kN•m）轴压比272.904271.024250.97090.96890.34183.6577.311
预留缝宽257.949271.964264.98585.98390.65588.3284.672
耗能材料刚度277.373272.372245.15392.45890.79181.71810.740
高跨比270.658250.670273.57090.21983.55791.1907.633
), ArticleFig(id=1245390275351261290, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 7, caption=

Level table of significance

, figureFileSmall=null, figureFileBig=null, tableContent=
项目Fj >F0.01F0.01≥ Fj >F0.05F0.05≥ Fj >F0.10F0.05≥ Fj >F0.25Fj≤ F0.25
影响显著性特别显著非常显著显著有一定影响无影响
符号表示* * * ** * ** **—
), ArticleFig(id=1245390275443535984, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表7, caption=

显著性水平表

, figureFileSmall=null, figureFileBig=null, tableContent=
项目Fj >F0.01F0.01≥ Fj >F0.05F0.05≥ Fj >F0.10F0.05≥ Fj >F0.25Fj≤ F0.25
影响显著性特别显著非常显著显著有一定影响无影响
符号表示* * * ** * ** **—
), ArticleFig(id=1245390275544199282, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 8, caption=

Variance analysis of the influence degree of factors

, figureFileSmall=null, figureFileBig=null, tableContent=
考核指标方差来源SSdfMSF临界值
屈服位移Δy预留缝宽6.13423.06751.117* * *F0.05 =19.00
耗能材料刚度5.00822.50441.733* * *F0.05 =19.00
高跨比1.44920.72512.083* *F0.10 =9.00
误差（轴压比）0.12020.060——
总和12.7118———
峰值荷载Pmax轴压比320.8762160.4380.962F0.25 =3.00
预留缝宽1564.0952782.0484.690*F0.25 =3.00
耗能材料刚度2602.06521301.0337.802*F0.25 =3.00
误差（高跨比）233.5032166.752——
总和4720.5398———
延性系数μ预留缝宽2.14821.07429.027* * *F0.05 =19.00
耗能材料刚度7.56223.781102.189* * * *F0.01 =99.00
高跨比1.70220.85123.000* * *F0.05 =19.00
误差（轴压比）0.07420.037——
总和11.4858———
初始侧向变形刚度K0预留缝宽52.779226.34039.022* * *F0.05 =19.00
耗能材料刚度10.71325.3577.936*F0.25 =3.00
高跨比20.110210.05514.896* *F0.10 =9.00
误差（轴压比）1.35020.675——
总和84.9538———
达到弹性位移角限值时的累计耗能Ee预留缝宽0.07520.0382.375F0.25 =3.00
耗能材料刚度0.04920.0251.563F0.25 =3.00
高跨比0.05620.0281.750F0.25 =3.00
误差（轴压比）0.03120.016——
总和0.2118———
达到弹塑性位移角限值时的累计耗能Ep轴压比98.533249.2673.010*F0.25 =3.00
耗能材料刚度200.4462100.2236.123*F0.25 =3.00
高跨比103.601251.8013.165*F0.25 =3.00
误差（预留缝宽）32.737216.369——
总和435.3178———
), ArticleFig(id=1245390275640668277, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表8, caption=

因素影响程度的方差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
考核指标方差来源SSdfMSF临界值
屈服位移Δy预留缝宽6.13423.06751.117* * *F0.05 =19.00
耗能材料刚度5.00822.50441.733* * *F0.05 =19.00
高跨比1.44920.72512.083* *F0.10 =9.00
误差（轴压比）0.12020.060——
总和12.7118———
峰值荷载Pmax轴压比320.8762160.4380.962F0.25 =3.00
预留缝宽1564.0952782.0484.690*F0.25 =3.00
耗能材料刚度2602.06521301.0337.802*F0.25 =3.00
误差（高跨比）233.5032166.752——
总和4720.5398———
延性系数μ预留缝宽2.14821.07429.027* * *F0.05 =19.00
耗能材料刚度7.56223.781102.189* * * *F0.01 =99.00
高跨比1.70220.85123.000* * *F0.05 =19.00
误差（轴压比）0.07420.037——
总和11.4858———
初始侧向变形刚度K0预留缝宽52.779226.34039.022* * *F0.05 =19.00
耗能材料刚度10.71325.3577.936*F0.25 =3.00
高跨比20.110210.05514.896* *F0.10 =9.00
误差（轴压比）1.35020.675——
总和84.9538———
达到弹性位移角限值时的累计耗能Ee预留缝宽0.07520.0382.375F0.25 =3.00
耗能材料刚度0.04920.0251.563F0.25 =3.00
高跨比0.05620.0281.750F0.25 =3.00
误差（轴压比）0.03120.016——
总和0.2118———
达到弹塑性位移角限值时的累计耗能Ep轴压比98.533249.2673.010*F0.25 =3.00
耗能材料刚度200.4462100.2236.123*F0.25 =3.00
高跨比103.601251.8013.165*F0.25 =3.00
误差（预留缝宽）32.737216.369——
总和435.3178———
), ArticleFig(id=1245390275720360057, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=EN, label=Table 9, caption=

Variance analysis of adjusted error terms

, figureFileSmall=null, figureFileBig=null, tableContent=
考核指标方差来源SSdfMSF临界值
屈服位移Δy轴压比0.12020.0600.083F0.25 =3.00
预留缝宽6.13423.0674.230*F0.25 =3.00
耗能材料刚度5.00822.5043.454*F0.25 =3.00
误差（高跨比）1.44920.725——
总和12.7118———
峰值荷载Pmax预留缝宽1564.0952782.0484.874*F0.25 =3.00
耗能材料刚度2602.06521301.0338.109*F0.25 =3.00
高跨比233.5032116.7520.728F0.25 =3.00
误差（轴压比）320.8762160.438——
总和4720.5398———
延性系数μ轴压比0.07420.0370.043F0.25 =3.00
预留缝宽2.14821.0741.262F0.25 =3.00
耗能材料刚度7.56223.7814.443*F0.25 =3.00
误差（高跨比）1.70220.851——
总和11.4858———
初始侧向变形刚度K0轴压比1.35020.6750.126F0.25 =3.00
预留缝宽52.779226.3904.926*F0.25 =3.00
高跨比20.110210.0551.877F0.25 =3.00
误差（耗能材料刚度）10.71325.357——
总和84.9538———
达到弹性位移角限值时的累计耗能Ee轴压比0.03120.0160.640F0.25 =3.00
预留缝宽0.07520.0381.520F0.25 =3.00
高跨比0.05620.0281.120F0.25 =3.00
误差（耗能材料刚度）0.04920.025——
总和0.2118———
达到塑性位移角限值时的累计耗能Ep预留缝宽32.737216.3690.332F0.25 =3.00
耗能材料刚度200.4462100.2232.034F0.25 =3.00
高跨比103.601251.8011.051F0.25 =3.00
误差（轴压比）98.533249.267——
总和435.3178———
), ArticleFig(id=1245390275821023355, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390262726406476, language=CN, label=表9, caption=

误差项调整后的方差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
考核指标方差来源SSdfMSF临界值
屈服位移Δy轴压比0.12020.0600.083F0.25 =3.00
预留缝宽6.13423.0674.230*F0.25 =3.00
耗能材料刚度5.00822.5043.454*F0.25 =3.00
误差（高跨比）1.44920.725——
总和12.7118———
峰值荷载Pmax预留缝宽1564.0952782.0484.874*F0.25 =3.00
耗能材料刚度2602.06521301.0338.109*F0.25 =3.00
高跨比233.5032116.7520.728F0.25 =3.00
误差（轴压比）320.8762160.438——
总和4720.5398———
延性系数μ轴压比0.07420.0370.043F0.25 =3.00
预留缝宽2.14821.0741.262F0.25 =3.00
耗能材料刚度7.56223.7814.443*F0.25 =3.00
误差（高跨比）1.70220.851——
总和11.4858———
初始侧向变形刚度K0轴压比1.35020.6750.126F0.25 =3.00
预留缝宽52.779226.3904.926*F0.25 =3.00
高跨比20.110210.0551.877F0.25 =3.00
误差（耗能材料刚度）10.71325.357——
总和84.9538———
达到弹性位移角限值时的累计耗能Ee轴压比0.03120.0160.640F0.25 =3.00
预留缝宽0.07520.0381.520F0.25 =3.00
高跨比0.05620.0281.120F0.25 =3.00
误差（耗能材料刚度）0.04920.025——
总和0.2118———
达到塑性位移角限值时的累计耗能Ep预留缝宽32.737216.3690.332F0.25 =3.00
耗能材料刚度200.4462100.2232.034F0.25 =3.00
高跨比103.601251.8011.051F0.25 =3.00
误差（轴压比）98.533249.267——
总和435.3178———
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柔性连接AAC填充墙钢框架抗震性能影响因素数值分析
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陈子夷 1 , 王旭峰 2
地震工程与工程振动 | 2024,44(5): 93-107
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地震工程与工程振动 | 2024, 44(5): 93-107
柔性连接AAC填充墙钢框架抗震性能影响因素数值分析
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陈子夷1 , 王旭峰2
作者信息
  • 1.华北水利水电大学 土木与交通学院，河南 郑州 450045
  • 2.中建六局土木工程有限公司，天津 300308

    • 陈子夷（1997—），女，硕士研究生，主要从事结构加固研究。E-mail：

通讯作者:

王旭峰（1995—），男，助理工程师，硕士，主要从事结构抗震研究。E-mail：
Numerical analysis of influence factors on seismic performance of flexible connection AAC infilled wall steel frame
Ziyi CHEN1 , Xufeng WANG2
Affiliations
  • 1.School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou 450045, China
  • 2.China Construction sixth Bureau Civil Engineering Co., Ltd., Tianjin 300308, China
doi: 10.13197/j.eeed.2024.0509
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摘要
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为分析不同因素变化对柔性连接蒸压加气混凝土（autoclaved areated concrete，AAC）砌体填充墙钢框架抗震性能影响的趋势和显著性，基于拟静力试验结果验证了建模方式及参数选取的可行性，采用ABAQUS建立9个有限元正交模型，对模型轴压比、预留缝宽、耗能材料刚度和高跨比进行变参分析。研究结果表明：预留缝宽、耗能材料刚度、高跨比和轴压比对结构抗震性能指标影响的显著性依次降低。整体上，增大预留缝宽，减小耗能材料刚度、高跨比以及轴压比对提高结构的抗震性能有利。实际应用中建议柔性连接AAC墙框间缝宽取值在40 mm左右，缝间填充材料的刚度宜在100~500 N/mm之间。

柔性连接  /  AAC填充墙  /  数值分析  /  影响因素  /  抗震性能指标  /  显著性

In order to analyze the trend and significance of the influence of different factors on the seismic performance of flexible connection autoclaved areated concrete(AAC) masonry filled wall steel frame structures, the feasibility of the modeling method and parameters selection was verified based on the results of pseudo-static tests, nine orthogonal finite element models were established by ABAQUS, and variable parameter analysis was carried out on axial compression ratio, reserved seam width, spring stiffness and height span ratio of models. The results show that the effects of reserved joint width, stiffness of energy-consuming materials, height span ratio and axial compression ratio on seismic performance of the structure decrease successively. On the whole, it is beneficial to increase the reserved joint width, reduce the stiffness of energy-consuming materials, high span ratio and axial compression ratio to improve the seismic performance of the structure. In actual application, the recommended value for the joint width between flexible connection AAC wall and frames is around 40 mm, and the stiffness of the filler between reserved joints is between 100~500 N/mm.

flexible connection  /  AAC infilled wall  /  numerical analysis  /  influence factor  /  seismic performance index  /  significance
陈子夷, 王旭峰. 柔性连接AAC填充墙钢框架抗震性能影响因素数值分析. 地震工程与工程振动, 2024 , 44 (5) : 93 -107 . DOI: 10.13197/j.eeed.2024.0509
Ziyi CHEN, Xufeng WANG. Numerical analysis of influence factors on seismic performance of flexible connection AAC infilled wall steel frame[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (5) : 93 -107 . DOI: 10.13197/j.eeed.2024.0509
正文
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0　引言
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近年来，国内外学者对框架填充墙组合体系的抗震性能通过“以强御强”和“以柔克刚”2种思想进行改善[1]。随着结构抗震韧性思想的提出，研究者开始注重墙框间接触关系的设计研究，提出“工程填充墙”概念[2]，以期提升确定地震下结构延性和承载力。之后不断有学者开展了柔性连接填充墙[3-5]、阻尼填充墙[6-7]和摇摆填充墙[8-9]等不同构造方案的研究。
研究表明影响该组合体系总刚度的因素有框架自身刚度、墙体自身刚度和墙框间构造连接的刚度[10]。受承载力限制，主体框架的刚度难以明显降低，削弱非结构构件填充墙体刚度和墙框间构造连接的刚度以降低结构震损和协调性能水平则成为必然选择。蒸压加气混凝土（autoclaved aerated concrete，AAC）砌块兼具结构—防火—保温一体化特点，耐久及抗震性能优异[11-13]。在采用AAC砌块削弱填充墙刚度效应的情形下，柔性连接替代刚性连接逐渐发展为必然趋势[14-15]。
关于填充墙框架结构抗震性能影响因素的研究，大量文献基于墙框刚性连接进行了单因素分析，通过改变结构轴压比、高跨比和墙体构造措施等，仅调整单一参数变化，研究其对结构抗震性能的影响[16-19]，难以评价各因素对抗震性能指标影响的显著性。对柔性连接AAC砌体填充墙钢框架抗震影响因素的研究尚为稀少。针对上述问题，文中基于拟静力试验结果对ABAQUS中柔性连接AAC填充墙钢框架三维数值模型建立和参数选取进行验证，结合正交设计法分析了轴压比、预留缝宽、缝间填充耗能材料刚度和高跨比对该柔性连接体系抗震性能影响的趋势和显著性。
1　数值模型建立
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1.1　模型试件概况
模型试件包含1榀空框架和1榀柔性连接AAC砌体填充墙钢框架，均以1∶2比例缩尺设计制做并进行拟静力试验，轴压比0.2。2榀框架尺寸均一致，梁净跨为1600 mm，柱净高为1400 mm，见图1。
空框架试件BF为对照试件。柔性连接试件IF墙框间设30 mm宽预留缝，见图1（b），缝间柔性构造参考减震可控式框架式保温填充墙的柔性连接结构[20]，预留缝间均以岩棉板作弹性耗能材料层填塞密实，以硅酮胶黏接材料层于墙框间以及两侧密封，沿AAC填充墙高度方向设置3道ɸ6水平拉结筋，水平长度为350 mm，拉结筋在竖向预留缝间于水平面方向弯曲成半圆弧形成伸缩缓冲部，拉结筋构造见图2，图中焊接点指该处与框架柱内侧翼缘表面进行焊接。
2榀框架均采用Q355B钢制做，拉结筋采用HPB235级，钢材性能测试结果见表1。钢框架梁、柱采用焊接H型钢，截面规格分别为H175 mm×100 mm×6 mm×8 mm、H150 mm×150 mm×8 mm×10 mm，框架各节点均以焊接连接，钢梁的翼缘、腹板与柱翼缘板分别采用对接焊缝、双面角焊缝焊接。试件IF填充墙体以B06级AAC砌块砌筑，砌块尺寸300 mm×100 mm×100 mm。制做与AAC填充墙同条件养护下的砌体试件测试抗压强度为3.53 MPa，弹性模量为1787 MPa。
1.2　模型建立
图3为2榀试件的三维数值分析模型。在ABAQUS/CAE中采用C3D8R实体单元建立钢框架填充墙模型，拉结钢筋采用T3D2桁架单元建立，在往复加载过程中试件IF中填充的岩棉板表现出良好的弹性变形及恢复能力，采用SPRINGA弹簧单元对弹性耗能材料层进行模拟。在Mesh模块中采用Structured技术对各部件划分尺寸为40 mm的六面体线性减缩积分单元网格。考虑到试验中填充墙未出现因灰缝抗剪强度不足而开裂，对填充墙模型采用整体式方法建立，以使模型在满足精度要求的前提下提高计算效率。墙框柔性连接中3道水平拉结筋的具体位置在模型BF中给出，见图3（a），模型BF数值计算时去除拉结筋。同时建立模型IF的对比模型IF-R，除墙框间以刚性连接外，其余参数与试件IF均一致，见图3（c）。
模型IF中各部件的相互作用在Interaction模块中定义。水平拉结筋与钢框架相接触的两点通过MPC约束绑定在一起，计算时两者间无相对移动，采用embedded方法将拉结筋嵌入到填充墙体中。AAC墙体底面与相接触位置的框架梁翼缘表面通过Tie约束绑定在一起。墙框间的岩棉板以每隔100 mm建立一个弹簧单元表示，线刚度取100 N/mm。根据试验加载方式，在框架左、右柱顶板的上表面各建立参考点RP-1和RP-2，在左框架柱外侧表面的相应位置处建立一参考点RP-3，将3个参考点的自由度分别耦合于相应表面。
在模型IF-R中，采用Surface-to-surface contact方式建立墙体侧表面、顶面与相应位置框架翼缘表面间的相互作用，翼缘表面为主表面，墙体表面为从表面、法向和切向行为分别以“硬”接触、“罚”摩擦来定义，摩擦系数取0.45[21]，定义摩擦系数各向同性。其余接触关系的定义与模型IF一致。
在Load模块中的initial分析步中选用“对称/反对称/完全固定”方式对钢框架两柱脚底面同时施加边界条件，定义钢框架柱脚完全固定，即U1=U2=U3=UR1=UR2=UR3=0。轴压比0.2在分析步Step1中定义，于参考点RP-1和RP-2同时施加竖向集中荷载，方向与ABAQUS/CAE界面中空间坐标系Z轴正向相反。水平循环荷载在分析步Step2中定义施加，通过幅值文件创建位移加载制度（图4）后赋予参考点RP-3。
1.3　材料本构
采用二折线随动强化本构建立钢材的应力-应变关系，如图5所示。AAC填充墙体材料特性采用ABAQUS中的混凝土损伤塑性（concrete damage plasticity，CDP）模型来构建，受压和受拉本构分别采用文献[22-23]提出的应力应变方程，如图6所示。
CDP模型中砌体塑性参数见表2，以能量等效模型[24]来确定塑性阶段AAC填充墙的拉、压损伤参数dt和dc，如图7所示。拟静力循环加载方向改变后，墙体裂缝会发生张开和闭合，压缩刚度在拉伸裂纹闭合后得以部分恢复，拉伸刚度在压裂后则无法恢复[25]，对CDP模型中的受拉刚度恢复因子取wt =0。文中基于编号为M-2的AAC砌体墙试验结果[26]对选取的砌体本构关系进行验证，受压刚度恢复因子wc不同取值下的计算结果见图8，取wc=0.4。
1.4　模型验证
空框架和柔性连接填充墙框架的试验破坏状态，如图9所示。模型BF、IF和IF-R发生破坏时的应力云图如图10所示。滞回曲线、骨架曲线对比如图11和图12所示。往复荷载循环作用下，模型BF、模型IF与相应试件的破坏特征基本一致，模型IF中填充墙体应力沿墙体四周边缘分布，在拉结筋锚固位置处应力明显较大，与拟静力试验结果一致。模型滞回曲线更为饱满，耗能较试验偏大，这是由于试验中存在试件制做安装误差、千斤顶卸压和螺栓松动等因素影响。模型与试验骨架曲线吻合良好，峰值荷载的计算值与试验值基本一致，为试验值的0.99~1.09倍。根据模拟结果可知，所用建模方法及参数具有可行性。
对比墙框刚性连接，柔性连接可显著减弱墙体对框架的斜撑效应，墙框间通过拉结筋传力，降低了整体结构的初始刚度，可承受更大的位移变形。
2　正交模型方案设计及计算结果
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2.1　模型参数与考核指标
正交设计法可将各因素水平借助正交表进行科学安排，以较少的试验量通过极差和显著性方差分析考核评价指标受各因素的影响程度。通过对已有研究分析，本文选取对填充墙框架结构抗震性能有较大影响的4个因素：轴压比（A）、预留缝宽（B）、耗能材料刚度（C）和高跨比（D），每个因素设置3个水平（表3），以分析柔性连接AAC砌体填充墙钢框架结构抗震性能评价中各因素的影响程度。
正交试验结果的评价考核是基于定量的极差、方差计算进行的。为便于计算分析各因素对该结构抗震性能的影响，本文以各正交模型整体结构的屈服位移Δy、峰值荷载Pmax、延性系数μ、初始侧向变形刚度K0、达到弹性位移角限值[θe]和弹塑性位移角限值[θp]时的累积耗能Ee和Ep作为考核指标。
2.2　模型方案设计
根据表3中确定的4个因素及相应水平数量，选用4因素3水平正交表L9（34）对各模型具体参数方案进行设计，见表4。
2.3　正交模型计算结果
根据表4中模型M1~M9的参数设置，在ABAQUS软件中分别建立对应模型，进行数值计算，得到9个模型的滞回曲线如图13所示。模型骨架曲线、刚度退化曲线分别如图14和图15所示。柔性连接AAC砌体填充墙钢框架模型各考核指标计算结果见表5。表中Δy、Pmax和μ的值均取推、拉两方向计算结果均值。
3　数值计算结果分析
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3.1　考核指标极差分析
各考核指标的极差分析结果见表6。表中K1、K2、K3分别为因素j（j取A、B、C或D）取值为水平1、2或3时，相应考核指标计算结果之和；k1、k2、k3分别为相应因素水平下，考核指标计算结果的均值。
由表6可知，轴压比（A）、预留缝宽（B）、耗能材料刚度（C）以及高跨比（D）等4个因素在所取的3个水平之间变化时，对柔性连接AAC填充墙钢框架的屈服位移Δy，其影响次序为B→C→D→A，即墙框间预留缝宽大小对结构屈服位移的影响最大。4个因素对结构峰值荷载Pmax大小的影响次序为C→B→A→D，即结构Pmax值的大小受柔性连接墙框预留缝间填充耗能材料刚度大小的影响最重，表5中的数值计算结果整体上表现为耗能材料刚度越大，其Pmax值越大，柔性连接填充墙框架结构越接近于刚性连接。对于结构的延性来说，4个因素影响次序为C→B→D→A，即耗能材料刚度对其影响最大。对结构初始刚度K0，4个因素的影响顺序依次为B→D→C→A，说明整体结构的初始刚度受墙框间缝宽大小影响最大，其次受主体结构高跨比的影响。结构受地震作用位移达到弹性位移角限值[θe]时，此时预留缝宽大小对结构的累计耗能有重要影响，其次为耗能材料刚度、高跨比，轴压比影响最小，即B→C→D→A；当位移达到弹塑性位移角限值[θp]时，因素影响次序为C→D→A→B。
各因素水平取值大小与考核指标间的趋势关系如图16所示。对于柔性连接AAC砌体填充墙钢框架结构，轴压比、耗能材料刚度和高跨比取值越大，对结构屈服时的位移值越不利，增大轴压比也会削弱结构延性，降低最大承载力，同时整体结构的初始刚度也会随着轴压比和墙框缝宽的增大出现降低。对整体结构的初始刚度、延性和峰值荷载，均随预留缝间填充材料刚度的增大而提高，说明地震时其直接影响墙体与框架间的相互作用程度。4个因素取值水平对结构达到限值[θe]和[θP]时的累积耗能影响趋势不一。
3.2　影响因素显著性检验
正交设计分析中，极差分析法直观简单，计算量小，但无法分清各因素对考核指标影响的显著性。因此，将轴压比、预留缝宽、耗能材料刚度和高跨比4个因素对柔性连接AAC砌体填充墙钢框架抗震性能考核指标的影响程度做进一步的显著性检验，即方差分析。
3.2.1　参数计算
影响因素显著性检验的参数计算，计算总离差平方和，如式（1）所示：
式中：SST为反映模型计算结果总差异的总离差平方和；xi为相应考核指标值；n为模型个数；Q为计算结果的平方和；P为计算结果和平方的均值。
各因素的离差平方和如式（2）所示：
式中：SSj为因素j的离差平方和；r为因素j的水平数；ki为i水平下模型相应考核指标计算结果的均值；Ki为i水平下模型相应考核指标计算结果的和。
计算误差的离差平方和如式（3）所示：
计算有限元模型计算结果的总自由度、各因素和误差自由度如式（4）所示：
式中：dfT为总自由度；dfj为因素j的自由度；dfe为误差自由度。
各因素的F值如式（5）所示：
式中：Fj为因素j的F值；MSj为因素j的均方；MSe为误差的均方。
3.2.2　显著性分析
依据检验水平α于F分布表中查找临界值Fα（fj，fe），将计算得到的Fj与其比较，以确定因素j的显著性，表7给出了不同α值下对应的显著性水平。
由于模型设计未考虑误差项的影响，为分析4种因素对各指标影响程度的显著性，先剔除各考核指标中4个因素均方值MS最小的一个，以其作为误差项，进行方差分析，结果见表8。以表8中影响显著性最小的因素作为误差项，加入先前剔除的因素继续方差分析，结果见表9。
根据上述步骤，对表5中各模型考核指标值进行参数计算，分析4个因素对柔性连接AAC砌体填充墙钢框架抗震性能影响的显著性。
对比表8和表9，以考核指标中4个因素均方值最小的一个作为误差项，分析其余因素对结构抗震性能的影响程度是可以接受的。可以发现，预留缝宽和耗能材料刚度对结构屈服位移的影响非常显著，高跨比对其也有显著影响。结构的延性受到耗能材料刚度大小的影响特别显著，同时预留缝宽、高跨比对其影响也非常显著。整体结构初始刚度受到墙框间缝宽大小的影响也非常显著。4个因素对各抗震性能指标影响的显著性分析表明，对柔性连接AAC砌体填充墙钢框架结构应特别重视墙框间的柔性构造，合理预留墙框间缝宽值及选取缝间填充材料。
3.2.3　4个因素对考核指标的影响率
基于工程实用性，对检验水平α取0.05，由式（6）计算各考核指标受4个因素的影响率δ[27]，如图17所示。
图17中，各考核指标中未出现的因素为误差项，当δ≥100%时，说明该指标受相应因素的影响显著。结构屈服位移受预留缝宽、耗能材料刚度变化的影响率分别为269.04%、219.65%；预留缝宽、弹簧刚度及高跨比对延性的影响率分别达到了152.77%、537.84%和121.05%；整体结构的初始刚度受到预留缝宽变化的影响率为205.38%；且高跨比变化对整体结构屈服位移、初始刚度的影响率也达到了63.59%和78.40%。因此，在实际工程应用中，应重视预留缝宽、耗能材料刚度和高跨比变化对柔性连接AAC砌体填充墙钢框架抗震性能的影响。
结合极差分析，综合考虑4个因素对柔性连接AAC填充墙钢框架各项考核指标影响的趋势和显著性，预留缝宽对结构性能的影响最为显著，缝宽在40 mm时性能最优；其次为耗能材料刚度的大小，柔性连接墙框预留缝间填充材料刚度的刚度不宜超过500 N/mm；相比于轴压比，高跨比对结构抗震性能的影响更大一些。
4　结论
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通过对9榀柔性连接AAC砌体填充墙钢框架模型进行变参数值分析，得到以下结论：
1）增大轴压比，结构各项抗震性能指标均呈下降趋势。在一定范围内增大墙框间缝宽对整体结构的屈服位移、峰值荷载均有提升，初始刚度明显下降，而延性的提升对缝宽限值有要求。减小耗能材料的刚度，会导致整体结构的初始刚度降低，同时其延性也会有所下降，并且峰值荷载也会相应减小，而结构的屈服位移则会增大。高跨比减小，整体结构的初始刚度、屈服位移及峰值荷载均有提高，但会削弱延性。对累积耗能，4个因素的影响趋势不一。
2）耗能材料刚度对柔性连接AAC填充墙钢框架延性的影响特别显著，对其屈服位移的影响非常显著。墙框间缝宽大小对整体结构初始刚度、延性和屈服位移的影响均非常显著。高跨比对结构延性、屈服位移也有非常显著的影响。4个因素对累积耗能的影响均不显著。
3）综合考虑4个因素对柔性连接AAC填充墙钢框架抗震性能的影响程度和趋势，影响程度由高到低依次为预留缝宽、耗能材料刚度、高跨比、轴压比。建议柔性连接墙框间缝宽取值在40 mm左右；预留缝间填充材料的刚度宜在100~500 N/mm之间。
基金
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  • 河南省科技攻关项目(212102310272)
  • 河南省高等学校重点科研项目(23A560006)
文献
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2024年第44卷第5期
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doi: 10.13197/j.eeed.2024.0509
  • 接收时间：2023-04-24
  • 首发时间：2026-03-30
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  • 收稿日期：2023-04-24
  • 修回日期：2023-06-14
基金
河南省科技攻关项目(212102310272)
河南省高等学校重点科研项目(23A560006)
作者信息
    1.华北水利水电大学 土木与交通学院，河南 郑州 450045
    2.中建六局土木工程有限公司，天津 300308

通讯作者:

王旭峰（1995—），男，助理工程师，硕士，主要从事结构抗震研究。E-mail：
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
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